- Browse by Author
Browsing by Author "Kuznetsov, Alexey"
Now showing 1 - 10 of 14
Results Per Page
Sort Options
Item Basal ganglia role in learning rewarded actions and executing previously learned choices: Healthy and diseased states(Public Library of Science, 2020-02-10) Mulcahy, Garrett; Atwood, Brady; Kuznetsov, Alexey; Psychiatry, School of MedicineThe basal ganglia (BG) is a collection of nuclei located deep beneath the cerebral cortex that is involved in learning and selection of rewarded actions. Here, we analyzed BG mechanisms that enable these functions. We implemented a rate model of a BG-thalamo-cortical loop and simulated its performance in a standard action selection task. We have shown that potentiation of corticostriatal synapses enables learning of a rewarded option. However, these synapses became redundant later as direct connections between prefrontal and premotor cortices (PFC-PMC) were potentiated by Hebbian learning. After we switched the reward to the previously unrewarded option (reversal), the BG was again responsible for switching to the new option. Due to the potentiated direct cortical connections, the system was biased to the previously rewarded choice, and establishing the new choice required a greater number of trials. Guided by physiological research, we then modified our model to reproduce pathological states of mild Parkinson's and Huntington's diseases. We found that in the Parkinsonian state PMC activity levels become extremely variable, which is caused by oscillations arising in the BG-thalamo-cortical loop. The model reproduced severe impairment of learning and predicted that this is caused by these oscillations as well as a reduced reward prediction signal. In the Huntington state, the potentiation of the PFC-PMC connections produced better learning, but altered BG output disrupted expression of the rewarded choices. This resulted in random switching between rewarded and unrewarded choices resembling an exploratory phase that never ended. Along with other computational studies, our results further reconcile the apparent contradiction between the critical involvement of the BG in execution of previously learned actions and yet no impairment of these actions after BG output is ablated by lesions or deep brain stimulation. We predict that the cortico-BG-thalamo-cortical loop conforms to previously learned choice in healthy conditions, but impedes those choices in disease states.Item Chaos and Robustness in a Single Family of Genetic Oscillatory Networks(2014-03) Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav IGenetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback.Item Circuit-level Mechanisms of EtOH-dependent dopamine release.(2017-06-30) DiVolo, Matteo; Morozova, Ekaterina; Lapish, Christopher; Kuznetsov, Alexey; Gutkin, Boris; Mathematical Sciences, School of ScienceAlcoholism is the third leading cause of preventable mortality in the world. In the last decades a large body of experimental data has paved the way to a clearer knowledge of the specific molecular targets through which ethanol (EtOH) acts on brain circuits. Yet how these multiple mechanisms play together to result in a dysregulated dopamine (DA) release under alcohol influence remains unclear. In this manuscript, we delineate potential circuit-level mechanisms responsible for EtOH-dependent increase and dysregulation of DA release from the ventral tegmental area (VTA) into nucleus accumbens (Nac). For this purpose, we build a circuit model of the VTA composed of DA and GABAergic neurons, that integrate external Glutamatergic (Glu) inputs to result in DA release. In particular, we reproduced a non-monotonic dose dependence of DA neurons firing activity on EtOH: an increase in firing at small to intermediate doses and a drop below baseline (alcohol-free) levels at high EtOH concentrations. Our simulations predict that a certain level of synchrony is necessary for the firing rate increase produced by EtOH. Moreover, EtOH effect on the DA neuron firing rate and, consequently, DA release can reverse depending on the average activity level of the Glu afferents to VTA. Further, we propose a mechanism for emergence of transient (phasic) DA peaks and the increase in their frequency in EtOH. Phasic DA transients result from DA neuron population bursts, and these bursts are enhanced in EtOH. These results suggest the role of synchrony and average activity level of Glu afferents to VTA in shaping the phasic and tonic DA release under the acute influence of EtOH and in normal conditions.Item Contribution of synchronized GABAergic neurons to dopaminergic neuron firing and bursting(APS Journals, 2016-10-01) Morozova, Ekaterina O.; Myroshnychenko, Maxym; Zakharov, Denis; di Volo, Matteo; Gutkin, Boris; Lapish, Christopher C.; Kuznetsov, Alexey; Mathematical Sciences, School of SciencePresented herein ventral tegmental area microcircuit model challenges the classical view that GABA neurons exclusively reduce dopamine neuron firing and bursting. Rather, high levels of synchrony amongst GABA neurons can produce increases in firing and bursting of the dopamine neuron. Dopamine bursting can be produced in the absence of bursty excitatory input, if the neuron receives transiently synchronized GABA input. We provide an explanation of the mechanisms whereby GABA neurons could contribute to dopamine neuron burst firing., In the ventral tegmental area (VTA), interactions between dopamine (DA) and γ-aminobutyric acid (GABA) neurons are critical for regulating DA neuron activity and thus DA efflux. To provide a mechanistic explanation of how GABA neurons influence DA neuron firing, we developed a circuit model of the VTA. The model is based on feed-forward inhibition and recreates canonical features of the VTA neurons. Simulations revealed that γ-aminobutyric acid (GABA) receptor (GABAR) stimulation can differentially influence the firing pattern of the DA neuron, depending on the level of synchronization among GABA neurons. Asynchronous activity of GABA neurons provides a constant level of inhibition to the DA neuron and, when removed, produces a classical disinhibition burst. In contrast, when GABA neurons are synchronized by common synaptic input, their influence evokes additional spikes in the DA neuron, resulting in increased measures of firing and bursting. Distinct from previous mechanisms, the increases were not based on lowered firing rate of the GABA neurons or weaker hyperpolarization by the GABAR synaptic current. This phenomenon was induced by GABA-mediated hyperpolarization of the DA neuron that leads to decreases in intracellular calcium (Ca2+) concentration, thus reducing the Ca2+-dependent potassium (K+) current. In this way, the GABA-mediated hyperpolarization replaces Ca2+-dependent K+ current; however, this inhibition is pulsatile, which allows the DA neuron to fire during the rhythmic pauses in inhibition. Our results emphasize the importance of inhibition in the VTA, which has been discussed in many studies, and suggest a novel mechanism whereby computations can occur locally.Item Distinct cortico-striatal compartments drive competition between adaptive and automatized behavior(Public Library of Science, 2023-03-21) Barnett, William H.; Kuznetsov, Alexey; Lapish, Christopher C.; Psychology, School of ScienceCortical and basal ganglia circuits play a crucial role in the formation of goal-directed and habitual behaviors. In this study, we investigate the cortico-striatal circuitry involved in learning and the role of this circuitry in the emergence of inflexible behaviors such as those observed in addiction. Specifically, we develop a computational model of cortico-striatal interactions that performs concurrent goal-directed and habit learning. The model accomplishes this by distinguishing learning processes in the dorsomedial striatum (DMS) that rely on reward prediction error signals as distinct from the dorsolateral striatum (DLS) where learning is supported by salience signals. These striatal subregions each operate on unique cortical input: the DMS receives input from the prefrontal cortex (PFC) which represents outcomes, and the DLS receives input from the premotor cortex which determines action selection. Following an initial learning of a two-alternative forced choice task, we subjected the model to reversal learning, reward devaluation, and learning a punished outcome. Behavior driven by stimulus-response associations in the DLS resisted goal-directed learning of new reward feedback rules despite devaluation or punishment, indicating the expression of habit. We repeated these simulations after the impairment of executive control, which was implemented as poor outcome representation in the PFC. The degraded executive control reduced the efficacy of goal-directed learning, and stimulus-response associations in the DLS were even more resistant to the learning of new reward feedback rules. In summary, this model describes how circuits of the dorsal striatum are dynamically engaged to control behavior and how the impairment of executive control by the PFC enhances inflexible behavior.Item Distinct Temporal Structure of Nicotinic ACh Receptor Activation Determines Responses of VTA Neurons to Endogenous ACh and Nicotine(Society for Neuroscience, 2020-07-07) Morozova, Ekaterina; Faure, Philippe; Gutkin, Boris; Lapish, Christoper; Kuznetsov, Alexey; Mathematical Sciences, School of ScienceThe addictive component of tobacco, nicotine, acts via nicotinic acetylcholine receptors (nAChRs). The β2 subunit-containing nAChRs (β2-nAChRs) play a crucial role in the rewarding properties of nicotine and are particularly densely expressed in the mesolimbic dopamine (DA) system. Specifically, nAChRs directly and indirectly affect DA neurons in the ventral tegmental area (VTA). The understanding of ACh and nicotinic regulation of DA neuron activity is incomplete. By computational modeling, we provide mechanisms for several apparently contradictory experimental results. First, systemic knockout of β2-containing nAChRs drastically reduces DA neurons bursting, although the major glutamatergic (Glu) afferents that have been shown to evoke this bursting stay intact. Second, the most intuitive way to rescue this bursting—by re-expressing the nAChRs on VTA DA neurons—fails. Third, nAChR re-expression on VTA GABA neurons rescues bursting in DA neurons and increases their firing rate under the influence of ACh input, whereas nicotinic application results in the opposite changes in firing. Our model shows that, first, without ACh receptors, Glu excitation of VTA DA and GABA neurons remains balanced and GABA inhibition cancels the direct excitation. Second, re-expression of ACh receptors on DA neurons provides an input that impedes membrane repolarization and is ineffective in restoring firing of DA neurons. Third, the distinct responses to ACh and nicotine occur because of distinct temporal patterns of these inputs: pulsatile versus continuous. Altogether, this study highlights how β2-nAChRs influence coactivation of the VTA DA and GABA neurons required for motivation and saliency signals carried by DA neuron activity.Item Dynamical ventral tegmental area circuit mechanisms of alcohol‐dependent dopamine release(Wiley, 2019) di Volo, Matteo; Morozova, Ekaterina O.; Lapish, Christopher C.; Kuznetsov, Alexey; Gutkin, Boris; Psychology, School of ScienceA large body of data has identified numerous molecular targets through which ethanol (EtOH) acts on brain circuits. Yet how these multiple mechanisms interact to result in dysregulated dopamine (DA) release under the influence of alcohol in vivo remains unclear. In this manuscript, we delineate potential circuit‐level mechanisms responsible for EtOH‐dependent dysregulation of DA release from the ventral tegmental area (VTA) into its projection areas. For this purpose, we constructed a circuit model of the VTA that integrates realistic Glutamatergic (Glu) inputs and reproduces DA release observed experimentally. We modelled the concentration‐dependent effects of EtOH on its principal VTA targets. We calibrated the model to reproduce the inverted U‐shape dose dependence of DA neuron activity on EtOH concentration. The model suggests a primary role of EtOH‐induced boost in the Ih and AMPA currents in the DA firing‐rate/bursting increase. This is counteracted by potentiated GABA transmission that decreases DA neuron activity at higher EtOH concentrations. Thus, the model connects well‐established in vitro pharmacological EtOH targets with its in vivo influence on neuronal activity. Furthermore, we predict that increases in VTA activity produced by moderate EtOH doses require partial synchrony and relatively low rates of the Glu afferents. We propose that the increased frequency of transient (phasic) DA peaks evoked by EtOH results from synchronous population bursts in VTA DA neurons. Our model predicts that the impact of acute ETOH on dopamine release is critically shaped by the structure of the cortical inputs to the VTA.Item IUPUI Center for Mathematical Biosciences(Office of the Vice Chancellor for Research, 2010-04-09) Boukai, Benzion; Chin, Ray; Dziubek, Andrea; Fokin, Vladimir; Ghosh, Samiran; Kuznetsov, Alexey; Li, Fang; Li, Jiliang; Rader, Andrew; Rubchinsky, Leonid; Sarkar, Jyotirmoy; Guidoboni, Giovanna; Worth, Robert; Zhu, LuodingAt-Large Mission: “to serve as an umbrella center for spearheading research and programmatic activities in the general bio-mathematics area” • promote and facilitate faculty excellence in mathematical and Computational research in the biosciences; • provide a mechanism and an environment that fosters collaborative research activities across the mathematical sciences and the life and health sciences schools at IUPUI— specifically with the IUSOM; • provide foundations and resources for further strategic development in targeted areas of mathematical and computational biosciences research; and • create greater opportunities and increase competitiveness in seeking and procuring extramural funding.Item Mathematical Models of Basal Ganglia Dynamics(2013-07-12) Dovzhenok, Andrey A.; Rubchinsky, Leonid; Kuznetsov, Alexey; Its, Alexander R.; Worth, Robert; Mukhin, EvgenyPhysical and biological phenomena that involve oscillations on multiple time scales attract attention of mathematicians because resulting equations include a small parameter that allows for decomposing a three- or higher-dimensional dynamical system into fast/slow subsystems of lower dimensionality and analyzing them independently using geometric singular perturbation theory and other techniques. However, in most life sciences applications observed dynamics is extremely complex, no small parameter exists and this approach fails. Nevertheless, it is still desirable to gain insight into behavior of these mathematical models using the only viable alternative – ad hoc computational analysis. Current dissertation is devoted to this latter approach. Neural networks in the region of the brain called basal ganglia (BG) are capable of producing rich activity patterns. For example, burst firing, i.e. a train of action potentials followed by a period of quiescence in neurons of the subthalamic nucleus (STN) in BG was shown to be related to involuntary shaking of limbs in Parkinson’s disease called tremor. The origin of tremor remains unknown; however, a few hypotheses of tremor-generation were proposed recently. The first project of this dissertation examines the BG-thalamo-cortical loop hypothesis for tremor generation by building physiologically-relevant mathematical model of tremor-related circuits with negative delayed feedback. The dynamics of the model is explored under variation of connection strength and delay parameters in the feedback loop using computational methods and data analysis techniques. The model is shown to qualitatively reproduce the transition from irregular physiological activity to pathological synchronous dynamics with varying parameters that are affected in Parkinson’s disease. Thus, the proposed model provides an explanation for the basal ganglia-thalamo-cortical loop mechanism of tremor generation. Besides tremor-related bursting activity BG structures in Parkinson’s disease also show increased synchronized activity in the beta-band (10-30Hz) that ultimately causes other parkinsonian symptoms like slowness of movement, rigidity etc. Suppression of excessively synchronous beta-band oscillatory activity is believed to suppress hypokinetic motor symptoms in Parkinson’s disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson’s disease exhibits complex intermittent synchronous patterns, far from the idealized synchronized dynamics used to study the delayed feedback stimulation. The second project of this dissertation explores the action of delayed feedback stimulation on partially synchronous oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a computational model of the basal ganglia networks which reproduces the fine temporal structure of the synchronous dynamics observed experimentally. Modeling results suggest that delayed feedback DBS in Parkinson’s disease may boost rather than suppresses synchronization and is therefore unlikely to be clinically successful. Single neuron dynamics may also have important physiological meaning. For instance, bistability – coexistence of two stable solutions observed experimentally in many neurons is thought to be involved in some short-term memory tasks. Bistability that occurs at the depolarization block, i.e. a silent depolarized state a neuron enters with excessive excitatory input was proposed to play a role in improving robustness of oscillations in pacemaker-type neurons. The third project of this dissertation studies what parameters control bistability at the depolarization block in the three-dimensional conductance-based neuronal model by comparing the reduced dopaminergic neuron model to the Hodgkin-Huxley model of the squid giant axon. Bifurcation analysis and parameter variations revealed that bistability is mainly characterized by the inactivation of the Na+ current, while the activation characteristics of the Na+ and the delayed rectifier K+ currents do not account for the difference in bistability in the two models.Item Modeling Temporal Patterns of Neural Synchronization: Synaptic Plasticity and Stochastic Mechanisms(2020-08) Zirkle, Joel; Rubchinsky, Leonid; Kuznetsov, Alexey; Arciero, Julia; Barber, JaredNeural synchrony in the brain at rest is usually variable and intermittent, thus intervals of predominantly synchronized activity are interrupted by intervals of desynchronized activity. Prior studies suggested that this temporal structure of the weakly synchronous activity might be functionally significant: many short desynchronizations may be functionally different from few long desynchronizations, even if the average synchrony level is the same. In this thesis, we use computational neuroscience methods to investigate the effects of (i) spike-timing dependent plasticity (STDP) and (ii) noise on the temporal patterns of synchronization in a simple model. The model is composed of two conductance-based neurons connected via excitatory unidirectional synapses. In (i) these excitatory synapses are made plastic, in (ii) two different types of noise implementation to model the stochasticity of membrane ion channels is considered. The plasticity results are taken from our recently published article, while the noise results are currently being compiled into a manuscript. The dynamics of this network is subjected to the time-series analysis methods used in prior experimental studies. We provide numerical evidence that both STDP and channel noise can alter the synchronized dynamics in the network in several ways. This depends on the time scale that plasticity acts on and the intensity of the noise. However, in general, the action of STDP and noise in the simple network considered here is to promote dynamics with short desynchronizations (i.e. dynamics reminiscent of that observed in experimental studies) over dynamics with longer desynchronizations.